The young, cancer-fighting biomathematician will object to that characterization, but history may not.

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Cancer is pretty smart. You'd think it wouldn't be -- you'd think, really, it should be pretty dumb, given that it originates in a single cell that behaves like a single cell, that behaves primitively, in comparison with all the cells around it. On the surface, a healthy cell is a lot smarter than a cancer cell; a healthy cell learns either to work, through a system of complicated cues and intricate cellular mechanisms, with the rest of the cells in the body, or it learns to die. A cancer cell, by comparison, is the lowest common denominator; it doesn't know anything -- it just wants to grow and proliferate. But a cancer cell is smart because evolution is smart. Evolution likes cells that just want to grow and proliferate, so it shares, with the cancer cells, its body of knowledge, its arsenal of tricks. Sure, cancer's pretty dumb when it starts out as a single cell with a single genetic mutation. But by the time it grows big enough, populous enough, to become apparent -- to show up on a routine screening or, heaven forbid, to hurt -- it's genius, man, because it's gone through a sequence of mutations, and with each mutation it's learned something about evading the body's defenses. And now it just has to evade medicine's. Which brings us to the question: Is medicine smart? And if it isn't -- if it isn't quite smart enough, even with all the desperate genius that humanity has poured into it -- what can we do to make it smarter?

Franziska Michor is pretty smart, too. If it takes a conspiratory sequence of six or seven mutations to produce a lethally intelligent cancer, consider how many random events have to line up to produce a woman who is, in no particular order:

a) twenty-five years old;

b) a slip of a thing, about a hundred pounds;

c) employed by the department of computational biology at Sloan-Kettering, the cancer hospital and research center in New York;

d) equipped with a Ph.D. in evolutionary biology from Harvard, which she earned at twenty-two;

e) determined to change the way modern medicine deals with cancer, so that it may truly be called modern;

f) disturbingly charming in her pronunciation of the dread word, cancer, which twists her lips and shows her teeth and becomes canszuh, a Germanism delivered at once bluntly and liltingly, with a rising stress -- an echo of American uptalk -- that emphasizes, in alternating shades, her youth, her blond beauty, her occasional awkwardness, and her supreme confidence; and

g) licensed to drive 18-wheelers in her native Austria.

Okay, the last item shows that perhaps not everything is random. Franziska is the daughter, on the paternal side, of Professor Peter Michor, a mathematician who is one of the world's foremost practitioners of differential geometry, a theoretical discipline that calls for the projection of shapes into infinite space and involves, in Franziska's words, "really big equations." In addition to sharing with his family the fruits of his elucubrations -- waking his wife and daughters with a ringing "Eureka!" when he solved a problem at three in the morning -- he shared his conviction that a classical education for a young woman should include lessons in:

a) cake baking;

b) ballroom dancing; and

c) truck driving.

"It was mostly because we had horses, and when you have three or four horses, you can no longer tow them with your car," Franziska says. "But he also thought that it would give me confidence. For the licensing test, I had to drive one of the big trucks through a slalom course. You do something like this at eighteen and you think you can do anything. I can also drive a tractor and a bulldozer." As a biologist whose orientation is both evolutionary and computational, Franziska is highly disposed in favor of the accidental as the deciding factor in life -- luck, or what she calls "stochastic processes." But it seems unlikely that if a family were to produce one Franziska accidentally, it would also produce, by the same method, someone like her sister, Johanna, who received her Ph.D. at twenty-five and currently works as a theoretical physicist, although she also holds her trucker's license, making the Michor sisters:

a) probably the only two sisters who are both licensed to drive trucks in Austria, as Franziska claims;

b) almost certainly the only two truck-driving sisters who received their Ph.D.'s at precociously young ages; and

c) without question the most quantitatively inclined of all the other truck-driving, Ph.D.-holding sister acts that might be out there, anywhere in the world.

So yeah, Franziska Michor is pretty smart, but that's not really the point, even though a certain amount of smarts helps, given what she's setting out to do. She's also pretty determined and pretty dedicated and pretty damn dauntless, but that's not the point, either, any more than are her talents at cake baking or ballroom dancing or the fact that she speaks six languages. No, the point is this: Franziska is, in the statistical sense of the word, improbable. She's to the general run of human capability what she is to truck driving in Austria. Her position on the bell curve of what people can and can't do is so far-flung as to seem exotic, even impossible. And she thinks medicine is -- though she would never use this word -- dumb. Not doctors, not scientists, and certainly not the people she's gotten to know at Princeton, where she was a theoretical biologist at the Institute for Advanced Study when she was nineteen, or at Harvard, or at Sloan. No, medicine -- at least in comparison with cancer, at least in comparison with the blind god of evolution. And what she wants to do is make it smarter. What she wants to do is teach it math.

You see, it's hard to be smart without math. It's not that you don't know anything; it's that what you know doesn't help you solve the problems that are staring you in the face. Take physics, for example. For centuries, physics was a descriptive science. It dedicated itself to understanding the movement of the spheres -- the mysteries of planetary motion -- but it could do little more than say, They move. It wasn't until Isaac Newton came along and invented calculus that physics could not just describe where the planets were yesterday but predict where they were going to be tomorrow. It wasn't until physics became a mathematical discipline that it began to get things right, began to be more than heroically perplexed and began charting the courses first of planets and then of atoms. And that's where medicine is right now. It's heroically perplexed. It's a descriptive science, which means that it's not really a science at all. Sure, it came a long way in the twentieth century. It triumphed in the twentieth century, in terms of being able to describe, for the first time, what is going on in the human body. But now, at the beginning of the twenty-first, it has a problem. "If you like science but don't like math, you go into medicine," Franziska says, and the problem with that is this: Evolution likes math. Cancer likes math. Both of them derive their power from mutations that increase exponentially over time. And so medicine is, well, outnumbered. It has battled cancer heroically for decades, but, as Franziska says, "even with all that time and all that money, it has not made very much progress, right?"

Right. Indeed, even where it has made progress, it hasn't made very much progress, as in the case of chronic myeloid leukemia. As cancers go, CML is pretty simple. It results from a defect in a single gene instead of a complex series of them. Its simplicity is what has allowed medicine to develop a drug for CML that is both very specific and very effective, a drug that targets the protein produced by the single defective gene. The drug is called Gleevec, and it's probably the best cancer drug that medicine's got. The only problem is that once people with CML stop taking it, the number of cancerous cells in their blood goes right back to the levels that existed before they started treatment, or even to much higher levels. It was a frustrating problem in what was considered a medical success story, and to figure out what was going wrong, Franziska did not do any laboratory experiments. Nor did she rely on any invasive procedures with CML patients. Instead, she got the numbers, then she did the math. She got blood counts from a collaborator in Australia and figured out how the cancer was responding to Gleevec over time. Once she had the data, she wrote down a series of equations that established, mathematically, the following:

Now, Franziska Michor likes math. She is a mathematician's daughter, after all. "When I was growing up, my father told me and my sister that we either had to study math or marry a mathematician. We said, Oh, no, anything but that! So we studied math." But her mother is a nurse, and Franziska's decided to use her father's skills to carry out her mother's mission. She does not want to spend her life doing proofs or teaching classes. "I prefer the thing I dedicate my life to to have practical applications. I want to discover something that helps people."

And so, although she is known for bringing mathematics to medicine, she is not a mathematician. She is, by her own description, "a theoretical evolutionary biologist working on cancer," and it sounds simple enough. It sounds, indeed, as if she's one of the many theoretical evolutionary biologists out there working on cancer, one of the community of theoretical evolutionary biologists out there working on cancer. The trouble is, she's not. There is no such thing -- no such field, no such course in medical schools, though she'd one day like to create it. Franziska Michor is pretty much the theoretical evolutionary biologist working on cancer. And if a lot of math is involved, that's because:

c) "without math, you make mistakes; there will be misunderstandings"; and

d) "you can't misunderstand an equation."

You would think the mathematicians would love it, would, at the very least, love her. They don't, some of them anyway. Oh, they invite her to speak at conferences, where she's often the keynote speaker. But she's often attacked, because what she's doing is too simple. "They think that what I'm doing is not math because it's too easy, because I'm not creating new techniques. They spend their time feeding huge equations into computers. They think that what I'm doing is trivial."

You would think that doctors would love it, because the simplicity that offends certain mathematicians is actually the goal of her work -- the reduction of complex systems into simple equations that would answer questions and help guide treatment. But a lot of them don't love what she's doing because a lot of them don't understand what she's doing; what seems simplistic to a mathematician can be baffling to a research clinician, and Franziska admits that even some doctors who've collaborated with her don't get the math. And so she's had to beg for data, even though the paper she's working on now offers a mathematical solution to a problem that has bedeviled oncologists for years -- the question of what's better for a patient:

a) low doses of chemotherapy sustained over time, or

b) high doses of chemotherapy interspersed with treatment "holidays" because of the toxic side effects.

The answer, as it turns out, is that under most conditions, with most cancers, the better course of treatment is b. What amazes Franziska, however, is not the result; it's that she is the first one to use equations to arrive at it. "It's a very controversial question," she says, "but there's been no quantitative analysis of what's the best approach to chemotherapy." And it's like that, she says, with question after basic question with cancer. There are statistics, of course; but statistics are, like medicine itself, descriptive. What she wants to do is use "the predictive force of mathematics" in cancer research and treatment, and make them "more quantitative." Which is why she left Harvard, where she was a junior fellow, and accepted Sloan-Kettering's offer. "It is where everybody goes," she says. "So there will be plenty of data." She is speaking of sick people, of course. She is speaking of people with cancer, and in the data she has asked for and already received from her many collaborations, she has seen just how smart cancer is, in the form of two-year-old data sets with this many patients left alive:

0.

She dresses like a college student. She wears low-rise bell-bottom jeans with the hems frayed from dragging on the ground. She wears wide belts, hippieish, and camisole tops. Her blond hair, parted on the right side, sweeps down over her left eye. When she blushes, she blushes pink, on her neck. All this underscores just how young she is, given the nature of her accomplishments. Yes, it's said that mathematics is a field that favors youth, and that the prime of a mathematician ends at thirty, and so Franziska, who very often looks no older than seventeen, realizes that even for her, time is an enemy. Of course, she already works hard, because of the data sets. One of the data sets she's been receiving is the data on patients with a type of brain cancer called glioblastoma. It is the most common form of brain cancer, and also the most dangerous, because it is the most diffuse. The tumor opens itself up in the brain like a fist opening to fingers, and by the time it is diagnosed, it is powered, Franziska says, "by hundreds of mutations." Often, glioblastoma is untreatable; generally it is inoperable; and almost inevitably it is fatal, with less than 50 percent of those who have it living six months past diagnosis. And one of the reasons for its intractability is its mathematical complexity; physicians faced with the tumor's brutal brand of exponential reasoning don't even know where to start. But Franziska does. She's been working to devise a mathematical model of glioblastoma, if only, she says, to create "a natural history of the tumor," a systematized vision of the evolution of chaos. It is another thing that she is doing that has never been done, and she is doing it so that maybe "we'd know which mutations to treat. That would at least give the people who have this disease something." Because right now, without the math, they have:

There is one moment when she wavers. She is tired, she's been looking for an apartment in Manhattan and facing the mathematical complexity of rent. She's thinking of all the grants she's going to have to write in order to justify her salary at Sloan and the salaries of the four people who are going to be working for her. She says that maybe she should spend a year making money in New York, that maybe she should lend her computational abilities to a hedge fund somewhere. Do that for a year or two, she thinks, and she would never have to write a grant application again, she would never have to beg . . . but then, she's smart enough to know that the thing that she would never do again is write an equation about cancer. "Well, maybe I wouldn't even be good at it," she says, and when she's asked if she's ever not been good at anything she's tried, she smiles and shrugs and says, Well, once, when she was playing the violin, one of her cats left the room. Then she gets serious. Playful, but serious.

"Maybe my success has been a matter of self-selection," she says. "Maybe I'm good at things I do because I do things that I know I'm going to be good at."

When she is told that she's good at things she does because she's smart, she asks, "How do you know I'm smart? Because I'm successful? Maybe you don't have to be smart to be successful. Maybe you just have to be brave."

In math, the quality of the model depends on the quality of its assumptions; the quality of the answer depends on the quality of the question. The answer, in fact, becomes inevitable once the question is stated properly. There is a deep question tugging at medicine, in regard to cancer, one that medicine has never been able to formulate properly. But maybe one of the answers is: